Russia has accused Ukraine of abducting two Russian servicemen on the annexed Crimea peninsula, but Kiev said it had merely detained two Ukrainian army deserters.

In a statement carried late Monday by local news agencies, the Russian defence ministry said servicemen Maxim Odintsov and Alexander Baranov were "illegally detained and removed from Crimea by Ukrainian security forces" on Sunday.

The Security Service of Ukraine (SBU) meanwhile said the two were "former Ukrainian servicemen who betrayed their oath and went to serve in the Russian military after the illegal annexation of Crimea".

The SBU added that the men stood accused of "desertion and treason" and had been detained at a checkpoint after crossing the administrative frontier between Russian-annexed Crimea and Ukraine.

It said the men had been caught after trying to bribe Ukrainian officials to obtain education certificates they needed to become officers in the Russian army.

A Russian Black Sea fleet spokesman told TASS the men were lured over the frontier apparently to receive higher education certificates and then immediately detained by SBU officers.

The two face jail sentences of up to 15 years if convicted of bribery and desertion.

Russia seized Crimea in 2014 by sending in thousands of special forces to take control of Ukrainian bases and holding a hastily organised referendum that was rejected by the international community.

The move shattered ties between the two ex-Soviet neighbours and sent relations between Moscow and the West plummeting to their lowest point since the Cold War.

In August, President Vladimir Putin accused Ukraine of attempting armed incursions into the disputed region.

Russia's security agency said at the time it had thwarted "terrorist attacks" in Crimea by Ukrainian military intelligence and beaten back armed assaults, but Kiev furiously denied the incidents.

The allegations ratcheted up tensions in the feud between Russia and Ukraine sparked by Moscow's seizure of the Black Sea peninsula and sparked fears of a wider conflict.